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" IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together... "
The Elements of Geometry, Symbolically Arranged - Side 37
av Great Britain. Admiralty - 1846
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The Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - 1993 - 298 sider
...will be parallel to one another. Proposition 28. // o straight line falling on two straight lines make the exterior angle equal to the interior and opposite angle on the same side, or the interior angles on the same side equal to two right angles, the straight lines will be parallel...
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The Durham University Journal, Volum 1

University of Durham - 1879
...[MARCH 22, 1879. 3. State Euclid's twelfth axiom. IB there any proposition of which it is the converse ? If a straight line fall upon two parallel straight lines it makes the alternate angles equal. 4. Prove that parallelograms on equal bases and between the same parallels are equal. In what sense...
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A Course in Modern Geometries

Judith Cederberg - 2004 - 441 sider
...straight lines will be parallel to one another. 28. If a straight line falling on two straight lines makes the exterior angle equal to the interior and opposite angle on the same side, or the interior angles on the same side equal to two right angles, the straight lines will be parallel...
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The Sheet-Metal Worker's Instructor

R. H. Warn, John G. Horner - 2002 - 284 sider
...of every triangle has the greater angle opposite to it. (Enc. I. 18.) (d) If a straight line fall on two parallel straight lines, it makes the alternate angles equal to one another. (Euc. I. 29.) (e) The opposite sides and angles of a parallelogram are equal to one another. (Euc....
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Designing Experiments & Games of Chance: The Unconventional Science of ...

William R. Shea - 2003 - 354 sider
...postulate of parallel lines to show that a straight line that falls on two parallel straight lines makes the exterior angle equal to the interior and opposite angle on the 'CEuvres de Pascal, I, p. 606, and pp. 574-575 for the first version. same side, and hence that the...
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